Nipher — Lcuo of Minimum DevicUion of Light by Prism. 135 



plane symmetrically located with respect to the axes r' and t. 

 This plane is determined by the condition r' = t, which makes 

 the entering and emergent rays symmetrical with respect to 

 the bounding surfaces of the refracting angle A. 

 Putting this condition iu (2) it reduces to 



sin 



* .— 



sin' ^ 



2 -H 2 co«^ 

 Since sin i = n sin r we have 



sin' A 



sin' r ^ 



2 4- 2 cos ^ 



The angles r = i' within the prism then become inde- 

 pendent of n, their value being dependent on A only. 



If the sines are regarded as the variables, equations (2) 

 and (3) represent an ellipse. Calling sin r' = y and 

 sin i = Xt those equations become, 



• y* -\- X* -\-2 y x<x» A=n* an* A. 



When the angle of the prism becomes zero the ellipse be- 

 comes the diagonal of a square whose sides are 2 n, the last 

 equation being y = — x. When A = 90^ the ellipse becomes 

 a circle whose equation is y* + a:' = n'. For intermediate 

 values of A the ellipse has the square whose side is 2 n as an 

 envelope, the major axis lying in the line whose equation is 

 y = — X. The minor axis always lies in the line whose 

 equation is y = x, which involves the condition « = r'. In 

 its general form (2) becomes 



y = — X cos A rb sin A \/ n- — x- 



The line y = dz n sin ^ laid off on the axis y and the line 

 whose equation is 



y=^ — X cos A 



are conjugate diameters of the ellipse. Those portions of 

 the ellipse corresponding to values of z or y greater than 



